Radiative decay engineering in hyperbolic metamaterials

One obvious application of the infinite photonic density of state that is the hallmark of hyperbolic materials is in controlling emission properties of dipoles coupled to the medium. In the Tutorials in Metamaterials chapter (info below) and in my thesis I provide the exciting details!

Slow light in hyperbolic metamaterials

HMMs exhibit negative group velocities in waveguides, making it possible to slow down or even stop light. This paper was the first to give a detailed description of slow light in planar waveguides, a full year before this topic became officially cool.

Reflection and transmission properties of hyperbolic structures

I provided models and calculations for the two groups doing proof-of-principle experiments in planar hyperbolic materials. The result of our work can be seen here and here.

Negative refraction and planar lenses in HMMs

Not olny does hyperbolic media support negative refraction, but, by some metrics, it performs better than the traditional plasmonic μ< 0 superlens. Details can be found in this paper and in Chapter 4 of my thesis.

The Hyperlens

After developing the basic computations for planar hyperbolic metamaterials, I helped adapt this formalism for the case of cylindrical structures. This turned out to be an intensely interesting problem in its own right, and it is currently being studied by Zubin Jacob. Here is the preprint of the original paper. It was one of the more intense paper-writing experiences of my career, but it did result in hundreds of citations!

Naturally-occuring hyperbolic materials

A little-appreciated fact about the hyperbolic dispersion relation is that under certain circumstances, it can occur in nature. When it does, it can be found typically in the mid-to-far IR (or even THz) in a narrow frequency band. Examples include bismuth at 50 micron wavelengths and sapphire around 20 microns. Here's a preprint that describes three known natural hyperbolic materials.